Let R be a relation on the set N≥0 given byR = {(a, b) : (b − a) is divisible by 6}Show that this is an equivalence relation

Question

Let R be a relation on the set N≥0 given byR = {(a, b) : (b − a) is divisible by 6}Show that this is an equivalence relation
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Solution 1

To show that a relation is an equivalence relation, we need to prove that it is reflexive, symmetric, and transitive.

  1. Reflexive: A relation R is reflexive if for every a in N≥0, (a, a) is in R. In this case, (b - a) would be (a - a) which equals 0. Since 0 is divisible by 6, the relation is refl Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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